Artificial Intelligence Planing (AIP)考试知识点复习

1 Classical Planing

Planning Domain Definition Language（PDDL）

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classical planning

• Domain-Independence Automated Planning=GPS general problem solving: create one planning algorithm that preforms sufficiently well on many application domain.
• plan validation: use VAL plan to independently verify if the plan is correct.
• path finding in very large deterministic transition systems

$$<S,s_0,S_{\ast },A,cost,T>$$
STRIPS:
$$<Variable,Initial,Goal,Action>$$

• optimal planning: only optimal plans are solutions
• satisficing planning: any plan is a solution, but cheaper plans are preferred

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big three planning approaches

• Graph/SAT Planing
• Symbolic Search Planning
• Heuristic State-Space Search

2 PDDL

first-order logic:一阶逻辑里面使用了大量所谓“限量词变量”（Quantified variables），比如：∃x（意思是存在一个变量x），限量词符号“∃”是把字母“E”从左向右反转过来产生的，其原本的意思的“Exist”（存在)；而限量词∀x（对所有的变量x），符号”∀“是将字母”A“从下向上反转而产生的，其原本意思是”All“（所有、全部）。在这里，逻辑符号”∃“和”∀“就是一阶逻辑的”限量词“（Quantifer）。
相关博文：什么是一阶逻辑

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下面会介绍PDDL语言中可以使用的一些常见语法

• PDDL2.1: Comparisons between numeric expressions are allowed as logical atoms:

(>=(fuel)(*(dist ?x ?y)(consumption)))

• PDDL2.1: extended with action durations

(= ?duration(/ (dist ?x ?y) (speed)))

举个例子：

• compiled using unary type predicates

(:objects a - block)
等价于
(:objects a)
(:init (BLOCK a))

• Quantor
  量词forall 和 exists,可以用and 和or 来代替了。
  

• Conditional effects “when”

forall (?x - block) (when (not (painted ?x) (color ?x)))

• negated preconditions

(not(p))变成了(not-p)

• increase&decrease
  
• plan metric

(: metric minimize (+ (* 2 total-time) (* 4 total-fuel-consumed)))

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接下来是PDDL2.2的内容

• derived predicates
  if…then…

(:derived (fed ?x) (exists ?y (and (connected ?x ?y) (fed ?y))))

• timed initial literals(TIL)
  独立于actions taken

(at 9 (shop-open)) 
(at 18 (not (shop-open)))

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• PDDL+ with temporal numeric change
• NUPDDL:uncertainty with oneof and unknown

(oneof (open_door d1) (open_door d2) (open_door d3))
(forall (?e - element_no) (unknown (element_value ?e)))

• obsevation
  

• PPDDL probabilistic
  
  
  
  至此，PDDL的代码应该是能看懂了。

3 PDDL+ (这一章节会进一步讲解上一章节的语法)

what make it hybird? 为什么PDDL+是混合的呢

• when actions or event are performed they cause instantaneous changes in the world;当执行动作的时候，世界立刻改变了。
• process are continuous changes. generate continuous updates in the world.
  

interact with a process while it runs #t

我们知道 这个球落地的时候，**(height ?b)**应该是全程大于零0的

我们来重新写一下这个球的过程，让球落下，弹起，接住。

1. First drop it action
   
2. watch it fall process
   
3. bounce event
   
4. catch it
   

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这里有一个简单的例子

4 eXplainable Planning

这一章就讲了几个explainable questions,感觉不太重要。
这一章不考试

5 planning with number

TIL(timed initial literals)

• 这个概念在PDDL2.2的时候介绍过，就是上文
• Allow us to model facts that become true, or false, at a specific time.‘Can use them to model deadlines or time windows.
• 这个TIL允许我们设定一些在某些时刻会变成true或者false的事实

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• 通过TIL，实现dealine：
  
  就是初始状态这是a，然后action的condition中at end设置一个a，然后初始状态设置一个某个时刻not-a.

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• 通过TIL，实现time windows
  
  跟上面一样

6 planning with preferences

• 满足hard goals 然后尽可能地满足preference
• sometime-before
• sometime-after
• preference
  (preference p1 (always(not(at B))))
  cost(p1) 这个是放弃这个preference所需要支付的cost
  

LTL(linear time logic)

• 有点像是temporal logic
  

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RELAXING NUMERIC EFFECTS

• Maintain bounds: upper and lower bound on each numeric variable
• 感觉好像是为了preference，为了主要的目的，有的时候可以放宽别的限制

distance to go & cost to go

• distance to go:minimum number of actions to call something a goal state
• cost to go:which forgo actions must be applied
• 
• 这里提到的distance-cost pairsis not all. All combinations of preferences would take ages. So use a greedy algorithm.

7 planning with motion

• TSP:travelling salesman problem
• 这部分没看懂讲了啥

8 考试卷子中的知识点（重要）

9 heuristic search planning

• Delete relaxaion：Estimate cost to goal by considering simpler planning task without negative side effects of actions.
• Abstraction：Estimate cost by projecting the state space to a smaller space.
• critical paths: Estimate cost by critical path length of a concurrent solution for a simplified problem.
• landmarks: an action set A is a landmark if all plans include an action from A. Compute a set of landmarks and use It to derive a cost estimate.

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这里提出了LP linear program：

LP with same objective value but role of constraints and variables interchanged.
one variable per operator

one constraint per landmark

minimum hitting set

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• network flows

Relaxed planning Graph(RPG)

state space

STN and snap action

local search

Local search is extremely prone to wandering down dead ends and having to backtrack a lot.

goal preference

RPG solution extraction

abstract state space

LP/COLIN